Space‐time dynamics of depositional systems: Experimental evidence and theoretical modeling of heavy‐tailed statistics

Abstract

[1] In depositional systems, channels migrate from one location to another, causing erosion and deposition at any given point in the domain. The durations of depositional and erosional events, as well as their magnitudes, control the structure of the stratigraphic record. In this study, we use high-resolution temporal surface elevation data from a controlled experiment to quantify the probability distributions of the processes that govern the evolution of depositional deltaic systems. Heavy-tailed statistics of erosional and depositional events are documented, indicating that a small but significant chance exists for the occurrence of extreme events. We show that the periods of inactivity, when neither deposition nor erosion occurs, follow a truncated Pareto distribution whose truncation scale is set by the mean characteristic avulsion time scale in the system. Further, we show that the heavy tails in the magnitudes of the erosional and depositional events are not preserved in the stratigraphic record, resulting instead in an exponential distribution for the bed sediment thickness. It is also shown that the temporal evolution of surface elevation exhibits self-similarity with a nonlinear spectrum of scaling exponents (multifractality) quantifying the complex dynamics of the system. Finally, we show how the results of this study can lead to improved diffusional models for surface evolution using the tools of fractional calculus.Citation: Ganti, V., K. M. Straub, E. Foufoula-Georgiou, and C. Paola (2011), Space-time dynamics of depositional systems: Experimental evidence and theoretical modeling of heavy-tailed statistics,

Quantitative bounds on morphodynamics and implications for reading the sedimentary record

“…4). For example, the deposition rate as measured from the sedimentary record in deltaic deposits is biased by stratigraphic incompleteness 8 over river-avulsion time scales 43 , which is on the order of thousands of years for large fluvial systems like the Mississippi. Thus, deltaic deposits likely record only environmental perturbations that manifest over large length scales.…”

Model predictions of long-lived storage of organic carbon in river deposits

“…Sediment grains will spend some portion of their time in transient storage within sediment deposits and the remain-der of their time in active transport associated with the river channel. We posit that the time spent in storage is much greater than the time spent in active transport (e.g., Sadler, 1981;Ganti et al, 2011) and, as a result, that the total transit time of sediments from source to sink can be approximated as the total time spent in storage. Since sediment grains likely enter and exit temporary storage reservoirs multiple times during transit, the total storage time can be separated into two components: (1) the number of times that grains enter and exit storage reservoirs and (2) the duration of each storage event.…”

Does the flow of information in a landscape have direction?

“…In landscapes undergoing a transient change-e.g., following a change in a forcing variable such as base-level-the long waiting times in the sediment motions may lead to time fractional derivatives in the governing transport equation [Schumer et al, 2009]. Experimental evidence for the existence of truncated heavy-tailed waiting times is reported in depositional systems under steady-state conditions [Ganti et al, 2011]. However, this non-locality in time will not affect the results presented here as the steady-state solutions remain the same for both time-fractional and non timefractional cases; the difference being in how fast the steadystate is reached.…”